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Homework Help

Lesson: Discussing the Existence of a Limit

In this lesson, we will learn how to find a limit and how to discuss the existence of a limit.

Sample Question Videos

05:12

Worksheet • 25 Questions • 1 Video

Q1:

Determine l i m π‘₯ β†’ 9 𝑓 ( π‘₯ ) , where

Q2:

Discuss the existence of l i m π‘₯ β†’ βˆ’ 6 𝑓 ( π‘₯ ) given 𝑓 ( π‘₯ ) = π‘₯ | π‘₯ + 7 | βˆ’ 3 .

  • A The limit exists and equals βˆ’ 9 .
  • B The limit does not exist because l i m π‘₯ β†’ βˆ’ 6 + 𝑓 ( π‘₯ ) does not exist.
  • C The limit exists and equals βˆ’ 3 .
  • D The limit does not exist because l i m π‘₯ β†’ βˆ’ 6 βˆ’ 𝑓 ( π‘₯ ) does not exist.
  • E The limit does not exist because l i m l i m π‘₯ β†’ βˆ’ 6 π‘₯ β†’ βˆ’ 6 βˆ’ + 𝑓 ( π‘₯ ) β‰  𝑓 ( π‘₯ ) .

Q3:

Given that determine l i m π‘₯ β†’ 1 𝑓 ( π‘₯ ) .

  • A 2 πœ‹
  • B2
  • C 1 2
  • D πœ‹ 2
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